Name ___________________________ Date _____________________ Show COMPLETE work on all questions. You CANNOT just solve them on a calculator. Any answer that is not supported by COMPLETE work will not be given credit. Questions 1-16 are 5 points each and Question 17 is worth 20 points. 1. Find each of the following limits, based on the graph, if they exist. lim f ( x) a. x 4 lim f ( x) b. x 8 c. x 8 d. lim f ( x) e. lim f ( x) lim f ( x) x 1 x6 2. lim x 2 3x 5 3. x2 1 x x 2 x 4. 3 x x 5 5. x 3 x 3 x 2 9 x 2 lim 2 6. Use f ( x ) = 3x 5 to find the following. f ( a h) f ( a ) a. Find the difference quotient h b. Determine lim h0 f ( a h) f ( a ) h lim lim 7. Differentiate y =5 x 2 3x 2 . 9. Find 11. Find f '( x ) and simplify. f ( x ) = x3 5 12. Differentiate: f ( x ) = 3 (1 3 x 2 ) 2 dy when y =( x 4)( x 2 3) dx 8. Find f '( x ) when f ( x) = 10. Differentiate f ( x) = 1 x4 x2 3 5x 13. Find an equation of the tangent line to the curve y = x 2 4 at the value x = 2. 14. Find intervals on which the function is increasing or decreasing. x2 f ( x) = ( x 1) 2 15. Test for relative extrema. Be sure to indicate which values are relative maximum or minimum values. You only need to identify the x values for this question. f ( x) =x 3 2 x 2 5 x 2 16. Find intervals on which the function is concave up or concave down. x 1 f ( x) = x 1 17. Find each of the requested parts below and then sketch the graph of the following function. Be sure to show clear, complete work for partial credit! (20 points) y =x3 2 x 2 8 x a) Intervals where the function increases: b) Intervals where the function decreases: c) Relative maximum points (write as an ordered pair): d) Relative minimum points (write as an ordered pair): e) Points of inflection: (just state x-values) f) Intervals where the function is concave up: g) Intervals where the function is concave down: h) x-intercepts: i) y-intercepts: j) Sketch the graph of the function making sure to show specifics from a-i on the previous page